<ol>
<li>When a positive integer, k, is divided by 7, the remainder is 6. What is the remainder when k+2 is divided by 7?</li>
</ol>
<p>The answer is 1, but even after reading over the detailed answer key I don't really understand the problem.</p>
<p>Thanks for the assistance!</p>
<p>k=6 (mod 7)
k+2= 1 (mod 7)</p>
<p>Answer is obviously 1</p>
<p>Or if modular arithmetic is not your thing…</p>
<p>just make up a number that fits. Like 13…13 divided by 7 is 1 r 6. Now check out 13+2=15 and 15 divided by 7 is 2 r 1. </p>
<p>If you are still not convinced, try starting with another number that fits…as long as the number you start with gives remainder 6, then the number you get when you add 2 will give remainder of 1 (remembering to use 7 as the divisor both times).</p>
<p>^My method takes ~10 seconds though. In case you were wondering I finish SAT math in half of the allotted time.</p>
<p>*sorry if I sound like I’m bragging…I just recommend solving the problem as efficiently as possible.</p>
<p>Thank you both for your help!</p>
<p>Sorry, GreedIsGood, but I’ve never seen the term “mod” before. Any chance you could clarify?</p>
<p>Ok basically this is ‘mod’</p>
<p>Example:</p>
<p>3 = 8 (mod 5)
3 = 13 (mod 5)
3 = 18 (mod 5)</p>
<p>So basically 3 is equivalent to 8 when they are divided by 5</p>
<p>Another way of thinking about it: 8 has remainder 3 when it is divided by 5.
13 has remainder 3 when it is divided by 5.</p>
<p>We would then say that 8=13 (mod 5)</p>